Algebra Examples

$\frac{\sqrt{16} - \sqrt{8}}{\sqrt{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}} - \sqrt{8}}{\sqrt{4}}$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4 - \sqrt{8}}{\sqrt{4}}$

Step 1.3

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.3.1

Factor $4$ out of $8$ .

$\frac{4 - \sqrt{4 (2)}}{\sqrt{4}}$

Step 1.3.2

Rewrite $4$ as $2^{2}$ .

$\frac{4 - \sqrt{2^{2} \cdot 2}}{\sqrt{4}}$

Step 1.4

Pull terms out from under the radical.

$\frac{4 - (2 \sqrt{2})}{\sqrt{4}}$

Step 1.5

Multiply $2$ by $- 1$ .

$\frac{4 - 2 \sqrt{2}}{\sqrt{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{4 - 2 \sqrt{2}}{\sqrt{2^{2}}}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4 - 2 \sqrt{2}}{2}$

Step 3

Cancel the common factor of $4 - 2 \sqrt{2}$ and $2$ .

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Step 3.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 2 - 2 \sqrt{2}}{2}$

Step 3.2

Factor $2$ out of $- 2 \sqrt{2}$ .

$\frac{2 \cdot 2 + 2 (- \sqrt{2})}{2}$

Step 3.3

Factor $2$ out of $2 (2) + 2 (- \sqrt{2})$ .

$\frac{2 (2 - \sqrt{2})}{2}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $2$ .

$\frac{2 (2 - \sqrt{2})}{2 (1)}$

Step 3.4.2

Cancel the common factor.

$\frac{2 (2 - \sqrt{2})}{2 \cdot 1}$

Step 3.4.3

Rewrite the expression.

$\frac{2 - \sqrt{2}}{1}$

Step 3.4.4

Divide $2 - \sqrt{2}$ by $1$ .

$2 - \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 - \sqrt{2}$

Decimal Form:

$0.58578643 \dots$